857 research outputs found
Solving the Hamilton-Jacobi Equation for General Relativity
We demonstrate a systematic method for solving the Hamilton-Jacobi equation
for general relativity with the inclusion of matter fields. The generating
functional is expanded in a series of spatial gradients. Each term is
manifestly invariant under reparameterizations of the spatial coordinates
(``gauge-invariant''). At each order we solve the Hamiltonian constraint using
a conformal transformation of the 3-metric as well as a line integral in
superspace. This gives a recursion relation for the generating functional which
then may be solved to arbitrary order simply by functionally differentiating
previous orders. At fourth order in spatial gradients, we demonstrate solutions
for irrotational dust as well as for a scalar field. We explicitly evolve the
3-metric to the same order. This method can be used to derive the Zel'dovich
approximation for general relativity.Comment: 13 pages, RevTeX, DAMTP-R93/2
Analysis of historical changes in soil fertility and organic matter levels of the North American Great Plains
Non-Peer Reviewe
A general T-matrix approach applied to two-body and three-body problems in cold atomic gases
We propose a systematic T-matrix approach to solve few-body problems with
s-wave contact interactions in ultracold atomic gases. The problem is generally
reduced to a matrix equation expanded by a set of orthogonal molecular states,
describing external center-of-mass motions of pairs of interacting particles;
while each matrix element is guaranteed to be finite by a proper
renormalization for internal relative motions. This approach is able to
incorporate various scattering problems and the calculations of related
physical quantities in a single framework, and also provides a physically
transparent way to understand the mechanism of resonance scattering. For
applications, we study two-body effective scattering in 2D-3D mixed dimensions,
where the resonance position and width are determined with high precision from
only a few number of matrix elements. We also study three fermions in a
(rotating) harmonic trap, where exotic scattering properties in terms of mass
ratios and angular momenta are uniquely identified in the framework of
T-matrix.Comment: 14 pages, 4 figure
Steady non-ideal detonations in cylindrical sticks of expolsives
Numerical simulations of detonations in cylindrical rate-sticks of highly
non-ideal explosives are performed, using a simple model with a weakly pressure
dependent rate law and a pseudo-polytropic equation of state. Some numerical issues
with such simulations are investigated, and it is shown that very high resolution
(hundreds of points in the reaction zone) are required for highly accurate (converged)
solutions. High resolution simulations are then used to investigate the qualitative
dependences of the detonation driving zone structure on the diameter and degree of
confinement of the explosive charge. The simulation results are used to show that,
given the radius of curvature of the shock at the charge axis, the steady detonation
speed and the axial solution are accurately predicted by a quasi-one-dimensional
theory, even for cases where the detonation propagates at speeds significantly below
the Chapman-Jouguet speed. Given reaction rate and equation of state models, this
quasi-one-dimensional theory offers a significant improvement to Wood-Kirkwood
theories currently used in industry
Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes
New algorithms for computing of asymptotic expansions for stationary
distributions of nonlinearly perturbed semi-Markov processes are presented. The
algorithms are based on special techniques of sequential phase space reduction,
which can be applied to processes with asymptotically coupled and uncoupled
finite phase spaces.Comment: 83 page
Hypersurface-Invariant Approach to Cosmological Perturbations
Using Hamilton-Jacobi theory, we develop a formalism for solving
semi-classical cosmological perturbations which does not require an explicit
choice of time-hypersurface. The Hamilton-Jacobi equation for gravity
interacting with matter (either a scalar or dust field) is solved by making an
Ansatz which includes all terms quadratic in the spatial curvature.
Gravitational radiation and scalar perturbations are treated on an equal
footing. Our technique encompasses linear perturbation theory and it also
describes some mild nonlinear effects. As a concrete example of the method, we
compute the galaxy-galaxy correlation function as well as large-angle microwave
background fluctuations for power-law inflation, and we compare with recent
observations.Comment: 51 pages, Latex 2.09 ALBERTA THY/20-94, DAMTP R94/25 To appear in
Phys. Rev.
Read-It: A Multi-modal Tangible Interface for Children Who Learn to Read
Multi-modal tabletop applications offer excellent opportunities for enriching the education of young children. Read-It is an example of an interactive game with a multi-modal tangible interface that was designed to combine the advantages of current physical games and computer exercises. It is a novel approach for supporting children who learn to read. The first experimental evaluation has demonstrated that the Read-It approach is indeed promising and meets a priori expectations
Scale invariant scalar metric fluctuations during inflation: non-perturbative formalism from a 5D vacuum
We extend to 5D an approach of a 4D non-perturbative formalism to study
scalar metric fluctuations of a 5D Riemann-flat de Sitter background metric. In
contrast with the results obtained in 4D, the spectrum of cosmological scalar
metric fluctuations during inflation can be scale invariant and the background
inflaton field can take sub-Planckian values.Comment: final version to be published in Eur. Phys. J.
Biodiversity loss underlies the dilution effect of biodiversity
The dilution effect predicts increasing biodiversity to reduce the risk of infection, but the generality of this effect remains unresolved. Because biodiversity loss generates predictable changes in host community competence, we hypothesised that biodiversity loss might drive the dilution effect. We tested this hypothesis by reanalysing four previously published meta-analyses that came to contradictory conclusions regarding generality of the dilution effect. In the context of biodiversity loss, our analyses revealed a unifying pattern: dilution effects were inconsistently observed for natural biodiversity gradients, but were commonly observed for biodiversity gradients generated by disturbances causing losses of biodiversity. Incorporating biodiversity loss into tests of generality of the dilution effect further indicated that scale-dependency may strengthen the dilution effect only when biodiversity gradients are driven by biodiversity loss. Together, these results help to resolve one of the most contentious issues in disease ecology: the generality of the dilution effect.Non peer reviewe
A confirmation of agreement of different approaches for scalar gauge-invariant metric perturbations during inflation
We revisit an extension of the well-known formalism for gauge-invariant
scalar metric fluctuations, to study the spectrums for both, the inflaton and
gauge invariant (scalar) metric fluctuations in the framework of a single field
inflationary model where the quasi-exponential expansion is driven by an
inflation which is minimally coupled to gravity. The proposal here examined is
valid also for fluctuations with large amplitude, but for cosmological scales,
where vector and tensor perturbations can be neglected and the fluid is
irrotacional.Comment: Version accepted in EPJC with new title. 11 pages, no figure
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